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5 days ago

Consider this polynomial, where a is an unknown real number.

Mathematics

1 answer:

PIT_PIT [9.1K]5 days ago

8 0

To find the value of 'a', follow these procedures: Braulio's synthetic division should proceed as follows: -1 | 1 5 a -3 11 Here, the remainder represents (a + 10). Hence, (a + 10) = 17, leading to a = 7. Braulio inaccurately calculated 'a' because he used 1 rather than -1. Zahra's calculation using the remainder theorem is as follows: p(x) = x⁴ + 5x³ + ax² - 3x + 11, p(-1) = (-1)⁴ + 5(-1)³ + a(-1)² - 3(-1) + 11 = 1 - 5 + a + 3 + 11 = (a + 10). Since the solution's remainder is 17, it follows that (a + 10) = 17, yielding a = 7. Zahra also made a mistake in determining 'a' due to incorrect handling of the powers of (-1).

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Choose the solutions of the following systems of equations x^2+y^2=6 and x^2-y=6

AnnZ [9099]

Answer:

The solutions are (-√6,0) and (√6,0)

(-√5,-1) and (√5,-1)

Step-by-step explanation:

We start with the equations:

${x}^{2} + {y}^{2} = 6$

and

${x}^{2} - y = 6$

Rearranging the second equation to make y the subject results in;

$y = {x}^{2} - 6$

Substituting into the first equation gives us:

${x}^{2} + ({x}^{2} - 6 )^2= 6$

$x = \pm \sqrt{6}$

and $x = \pm \sqrt{5}$

The solutions remain as (-√6,0) and (√6,0)

(-√5,-1) and (√5,-1)

7 0

29 days ago

Bridgette opened a store credit card to purchase a business suit for $463. She put the entire purchase on the credit card. Her A

Inessa [9000]

Begin by determining the monthly interest rate as follows:
$\frac{14.99}{12}=1.25$
<span>Each month, we deduct the monthly rate and the 5% payment from $463, leading to the following formula:</span>
$463(1-(0.05+0.0125))^3=463\times0,9375^3\\=381.5$
<span>
Therefore, after three months, Bridgette will have a remaining balance of $381.5 in her account.</span>

5 0

26 days ago

A gift box has dimensions of: 8 1 2 inches, 5 1 2 inches, and 2 1 2 inches, respectively. how many cubes with side lengths of 1

Inessa [9000]

Lengthwise count of 1/2-inch cubes = 8 1/2 ÷ 1/2 = 17
Widthwise count of 1/2-inch cubes = 5 1/2 ÷ 1/2 = 11
Heightwise count of 1/2-inch cubes = 2 1/2 ÷ 1/2 = 5

Total number of 1/2-inch cubes = 17 x 11 x 5 = 935

------------------------------------------------------------
Answer: 935 1/2-inch cubes are required.
------------------------------------------------------------

7 0

4 days ago

What is the positive solution to the equation 0 = –x2 + 2x + 1? Quadratic formula: x = StartFraction negative b plus or minus St

zzz [9080]

Answer:

$1+\sqrt{2}$

Step-by-step explanation:

Consider a quadratic equation given by

$ax^2+bx+c=0$ .... (1)

The quadratic formula then is

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

The quadratic equation provided is

$0=-x^2+2x+1$

This can be expressed as

$-x^2+2x+1=0$ .... (2)

By comparing (1) and (2), we derive:

$a=-1,b=2,c=1$

Plug these values into the quadratic formula.

$x=\dfrac{-2\pm \sqrt{2^2-4(-1)(1)}}{2(-1)}$

$x=\dfrac{-2\pm \sqrt{4+4}}{-2}$

$x=\dfrac{-2\pm \sqrt{8}}{-2}$

$x=\dfrac{-2\pm 2\sqrt{2}}{-2}$

Factoring out common elements.

$x=\dfrac{-2(1\pm \sqrt{2})}{-2}$

$x=1\pm \sqrt{2}$

The two solutions are

$x=1+\sqrt{2}$ and $x=1-\sqrt{2}$

We recognize that

$\sqrt{2}=1.41$

Thus,

$1$

Consequently, root $x=1+\sqrt{2}$ is positive while $x=1-\sqrt{2}$ is negative.

9 0

21 day ago

Read 2 more answers

On his first day of school, Kareem found the high temperature in degrees Fahrenheit to be 76.1°. He plans to use the function to

Inessa [9000]

The formula to convert Fahrenheit to Celsius is:

Celsius = (Fahrenheit - 32) x 5/9

C(76.1) = (76.1 - 32) x 5/9
= (44.1) x 5/9
= 24.5

Hence, 76.1°F is equal to 24.5°C.

5 0

9 days ago

Read 2 more answers